Study of hard double-parton scattering in four-jet events in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS experiment

Inclusive four-jet events produced in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=7$ TeV are analysed for the presence of hard double-parton scattering using data corresponding to an integrated luminosity of 37.3 pb${}^{-1}$, collected with the ATLAS detector at the LHC. The contribution of hard double-parton scattering to the production of four-jet events is extracted using an artificial neural network, assuming that hard double-parton scattering can be approximated by an uncorrelated overlaying of dijet events. For events containing at least four jets with transverse momentum $p_{\mathrm{T}}\ge 20$ GeV and pseudorapidity $\eta \le 4.4$, and at least one having $p_{\mathrm{T}}\ge 42.5$ GeV, the contribution of hard double-parton scattering is estimated to be $f_{$\mathrm{D}\mathrm{P}\mathrm{S}$} = 0.092 ^{+0.005}{-0.011} ($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) ^{+0.033}{-0.037} ($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}$)$. After combining this measurement with those of the inclusive dijet and four-jet cross-sections in the appropriate phase space regions, the effective overlap area between the interacting protons, ${\sigma }_{\mathrm{e}\mathrm{f}\mathrm{f}}$, was determined to be $\sigma_{$\mathrm{e}\mathrm{f}\mathrm{f}$} = 14.9 ^{+1.2}{-1.0} ($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) ^{+5.1}{-3.8} ($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}$)$ mb. This result is consistent within the quoted uncertainties with previous measurements of ${\sigma }_{\mathrm{e}\mathrm{f}\mathrm{f}}$, performed at centre-of-mass energies between 63 GeV and 8 TeV using various final states, and it corresponds to $21_{-6}^{+7}$% of the total inelastic cross-section measured at $\sqrt{s}=7$ TeV. The distributions of the observables sensitive to the contribution of hard double-parton scattering, corrected for detector effects, are also provided.